Nuprl Lemma : fpf-join-idempotent
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. (f ⊕ f = f ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
deq_wf,
fpf_wf,
filter_is_nil,
bnot_wf,
deq-member_wf,
l_all_iff,
l_member_wf,
not_wf,
assert_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-deq-member,
append_nil_sq,
subtype_rel_list,
top_wf,
subtype_rel-deq,
member_wf,
equal_wf,
set_wf,
list-subtype,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. (f \moplus{} f = f)
Date html generated:
2015_07_17-AM-09_19_13
Last ObjectModification:
2015_01_28-AM-07_50_08
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